As far as I recall, Rhythmbox doesn't rip CDs on its own. If you can do it through Rhythmbox, then it will be running another programme to do the ripping for it.
On my PC, I use sound-juicer. It's been a while since I used Mint, so I can't remember how to install software off the top of my head, but in Ubuntu the package is confusingly named just "Audio CD Extractor". But running "sudo apt-get install sound-juicer" in the terminal should install it if it's not already installed