This is very annoying that ffmpeg is missing from Linux Mint! They have ffmpeg2theora which is a totally different codec and does not work as ffmpeg does at all (it is basically totally different).
However on Linux Mint 17 I was able to use a Ubuntu PPA and sucessfully install ffmpeg!
You can update your system with unsupported packages from this untrusted PPA by adding ppa:mc3man/trusty-media to your system's Software Sources. (Read about installing)
sudo add-apt-repository ppa:mc3man/trusty-media sudo apt-get update
Solution Now Install ffmpeg!
sudo apt-get install ffmpeg