It depends on how thorough you want to be. Running GParted and creating a new partition table then reinstalling Mint will eliminate all addresses and directories but the data itself can still be retrieved by anyone with the right knowledge and software.
Programs like Active Killdisk( http://active-kill-disk-hard-drive-eraser.filecart.com/
) and Darik's Boot and Nuke ( http://www.dban.org/
) will overwrite the disk with anything from one pass of all zeros to 34 passes of random characters followed by one pass of all zeros. The idea is, the more times the data is overwritten, the harder it is to retrieve.
The downside is time. It can take 1-3 hours to do a single pass all zeros wipe, depending on the size of the drive and the speed of the computer. And, of course, more passes means more time.