Welcome to Mint!
Yes, you have discovered one of the last few areas in which Linux is still not 'getting it,' audio!
However, on your taskbar there may be a speaker symbol, double click on it to reveal the alsamixer.
When that window opens, you may have tabbed areas, (at least playback) available.
In the playback tab, look for a headphone listing. (I you don't have a headphone channel listed...click on Preferences in the alsamixer window, and click on the headphone checkbox to make it available in the alsamixer.)
In the headphone channel Are the sliders up? Is there a red x (indicating mute is on) over the speaker icon at the bottom of the headphone column? (just click once to un-mute)
Hope this helps.
Malachi 3:10 NRSV
...says the LORD of hosts... I will not open...windows...for you...
Linux user since 2001 pda; 2006 lappy