You have some options.
BTW If you encounter any problems, stop and ask on this forum for fixes/clarifications
If you have an external disk big enough to hold your data files you could do a bulk copy of the relevant data directories.
Alternatively, if you don't have too much data you could just copy to a USB stick.
Please note that system directories such as /etc, /usr etc should be considered as corrupt and should not be restored - you could copy /var/log, but only to look at it - don't restore it!
Boot from live Mint USB/DVD
You will need to create a file system on any external device - I suggest you use
gparted to do this.
gparted will also show the partitions on your hard disk - make a note of which partition(s) contain files of interest to you.
Exit from
gparted
Then, open a terminal screen.
Remove the external disk or USB stick and re-insert it.
Because it now has a file system it should get automounted.
To access a disk partition you need to mount it - try
Code:
sudo mount /dev/sdax /mnt
You shouldn't need a password
Note that I'm assuming your hard disk is sda and 'x' is the partition number.
The mountpoint /mnt (directory) will then appear to hold all the data files and directories on your hard disk.
You should be able to look at /mnt in your GUI file manager.
This is the time to copy all your vital files to the external media...
When you have finished don't forget to do
Finally, take the install Mint option, overwriting everything.
After updates/upgrades have been done + adding/removing selected packages you will be able to copy back your data.
Then take a proper backup.