You're problem is probably worse then you expect, but not so bad you will lose your files.
For your benefit (you have 17, I have 17.1, I presume cinnamon version), I ran the same command to remove pulseaudio to see what else would be removed:
cinnamon cinnamon-bluetooth cinnamon-control-center cinnamon-dbg
libcanberra-pulse mint-meta-cinnamon pulseaudio pulseaudio-module-bluetooth
Basically, you completely removed cinnamon. You will need to install all of these to get a functioning system and even then it might not work.
but, it gives a better chance then just installing pulseaudio!
Whatever happens, your information is still safe, you can use a tty to copy the data elsewhere. But try the above first.