I have CUDA tasks running on:
Ubuntu 14.04 with a GTX770
Lubuntu 13.10 with a GTX570
so it *can* be done!
Are you installing the nvidia drivers from the repository, or downloading directly from the nvidia website? Either way will work, but the mechanisms are different.
When I've downloaded from the repository, these are the commands I used (in a plain ol' terminal window):
sudo apt-get --purge remove xserver-xorg-video-nouveau
sudo add-apt-repository ppa:ubuntu-x-swat/x-updates
sudo apt-get update && sudo apt-get install nvidia-current nvidia-settings
Then, reboot the machine.
To go the other route, point your web browser at nvidia.com and there will be a "support" menu at the top of the page that will take you to a page with a "download drivers" button. Click that. The next page has a "manually find drivers" section where you pick your OS, card type, and so on, and a "search" button. After the search, you'll get to a page with a "download" button, which will download a file called something like "NVIDIA-Linux-x86_64.340.65.run", about 60 or 70 MB. You then need to run that file with something like:
chmod +x NVIDIA-Linux-x86_64.340.65.run
./NVIDIA-Linux-x86_64.340.65.run (may need "sudo" before that?)
But, there is a twist. You can't be running a window manager when executing that ".run" script. I hesitate to advise how to kill the window manager on Mint, but on plain Ubuntu, the command is:
sudo service lightdm stop
Then run the ".run" script (it takes a while), and then reboot the box. I've done all this remotely logged-in via "ssh" from a Mac.
All in all, I think the first option is safer/easier, but may not get you the latest version (which sometimes is a good thing!).
Hopefully I didn't just "brick" your machine :0 It's good to have a second machine nearby to do web searches to resolve problems if/when they arise. Updated software on Linux appears weekly (at least), and the updates work flawlessly, in my experience.
If I can be of any further assistance, you know where to reach me :-)