I did run apt-get update i did it again and posted results below.
Oh i failed to answer your previous question. Im using the LMDE 3/2014. LMDE-2 has dependency problems installing Compiz Which makes my home theater system look awesome.
$ sudo apt-get update
[sudo] password for xxxxx:
Ign
http://packages.linuxmint.com debian InRelease
Ign
http://extra.linuxmint.com debian InRelease
Get:1
http://packages.linuxmint.com debian Release.gpg [198 B]
Hit
http://liquorix.net sid InRelease
Get:2
http://packages.linuxmint.com debian Release [16.7 kB]
Ign
http://extra.linuxmint.com debian Release.gpg
Hit
http://liquorix.net sid/main Sources
Hit
http://liquorix.net sid/main amd64 Packages
Hit
http://liquorix.net sid/main i386 Packages
Get:3
http://extra.linuxmint.com debian Release [2,275 B]
Get:4
http://packages.linuxmint.com debian/main amd64 Packages [26.1 kB]
Ign
http://extra.linuxmint.com debian/main amd64 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing InRelease
Get:5
http://packages.linuxmint.com debian/upstream amd64 Packages [16.1 kB]
Ign
http://extra.linuxmint.com debian/main i386 Packages/DiffIndex
Get:6
http://packages.linuxmint.com debian/import amd64 Packages [55.4 kB]
Ign
http://liquorix.net sid/main Translation-en_US
Ign
http://liquorix.net sid/main Translation-en
Hit
http://debian.linuxmint.com testing/updates InRelease
Get:7
http://packages.linuxmint.com debian/main i386 Packages [26.1 kB]
Get:8
http://packages.linuxmint.com debian/upstream i386 Packages [16.1 kB]
Get:9
http://packages.linuxmint.com debian/import i386 Packages [55.4 kB]
Hit
http://debian.linuxmint.com testing InRelease
Hit
http://debian.linuxmint.com testing/main amd64 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/contrib amd64 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/non-free amd64 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/main i386 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/contrib i386 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/non-free i386 Packages/DiffIndex
Hit
http://debian.linuxmint.com testing/contrib Translation-en/DiffIndex
Get:10
http://extra.linuxmint.com debian/main amd64 Packages [20 B]
Hit
http://debian.linuxmint.com testing/main Translation-en/DiffIndex
Hit
http://debian.linuxmint.com testing/non-free Translation-en/DiffIndex
Get:11
http://extra.linuxmint.com debian/main i386 Packages [20 B]
Ign
http://extra.linuxmint.com debian/main Translation-en_US
Ign
http://extra.linuxmint.com debian/main Translation-en
Hit
http://debian.linuxmint.com testing/updates/main amd64 Packages
Ign
http://packages.linuxmint.com debian/import Translation-en_US
Ign
http://packages.linuxmint.com debian/import Translation-en
Ign
http://packages.linuxmint.com debian/main Translation-en_US
Hit
http://debian.linuxmint.com testing/updates/contrib amd64 Packages
Ign
http://packages.linuxmint.com debian/main Translation-en
Ign
http://packages.linuxmint.com debian/upstream Translation-en_US
Ign
http://packages.linuxmint.com debian/upstream Translation-en
Hit
http://debian.linuxmint.com testing/updates/non-free amd64 Packages
Hit
http://debian.linuxmint.com testing/updates/main i386 Packages
Hit
http://debian.linuxmint.com testing/updates/contrib i386 Packages
Hit
http://debian.linuxmint.com testing/updates/non-free i386 Packages
Hit
http://debian.linuxmint.com testing/updates/contrib Translation-en
Hit
http://debian.linuxmint.com testing/updates/main Translation-en
Hit
http://debian.linuxmint.com testing/updates/non-free Translation-en
Hit
http://debian.linuxmint.com testing/main amd64 Packages
Hit
http://debian.linuxmint.com testing/non-free amd64 Packages
Hit
http://debian.linuxmint.com testing/main i386 Packages
Hit
http://debian.linuxmint.com testing/non-free i386 Packages
Ign
http://debian.linuxmint.com testing/main Translation-en_US
Ign
http://debian.linuxmint.com testing/main Translation-en
Ign
http://debian.linuxmint.com testing/non-free Translation-en_US
Ign
http://debian.linuxmint.com testing/non-free Translation-en
Fetched 214 kB in 7s (27.6 kB/s)
Reading package lists... Done
$ sudo apt-get install linux-image-liquorix-amd64 linux-headers-liquorix-amd64
Reading package lists... Done
Building dependency tree
Reading state information... Done
linux-image-liquorix-amd64 is already the newest version.
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
linux-headers-liquorix-amd64 : Depends: linux-headers-3.19-2.dmz.2-liquorix-amd64 (= 3.19-2) but it is not going to be installed
E: Unable to correct problems, you have held broken packages.
$
When i try to install the missing dependency using package manager the results are attached in the screenshots