1) Backup your /home folder if you don't have a /home partition.
2) Boot from a Live install (either DVD or USB thumb drive) for LM13.
3) If everything works in the Live session (sound, video modes, keyboard, pointing device, etc.), then proceed with an installation.
4) Answer the preliminary questions: (language, keyboard, set system time, etc.) until it asks you how you want to install.
5) Select (I believe it is called) Other when it asks how you want to install.
6) Simply choose your old LM11 partitions and designate the usage as /, swap, (and /home if you have one) and tell the program to format / in EXT4 or whatever file-system you want to use.
7) Proceed as normal, following the screen prompts.
LMDE Mate 64-bit, LM16 Mate 64-bit
Debian Xfce 64-bit, Xubuntu 13.10 64-bit, Xubuntu Trusty Tahr 64-bit, Antergos Xfce 64-bit, PCLinuxOS LXDE 64-bit