Where does Gnome Color Manager store the ICM or ICC files?

You can find your colour profiles as ICC files in ~/.local/share/icc. (Where ~ is your home folder).

The files have slightly cryptic names, but you can open them (with the ICC Profile Installer) to see a little more information. Otherwise, open the Color settings panel and click the View details button with a profile selected. The "Filename" field in that dialog should point you in the right direction.

You don't have to search for it in nautilus.

Click HERE (if the manufacturer is HP/COMPAQ-otherwise go to your monitors' website), Look up your monitor in the search bar at the top, once you get some results click on the little blue link titled "Drivers & Software". You should have results within the first 2-3 items in the search results. Look for the one that says "Software" at the far right side, click and download the "you're_file.exe".

Run it, go to the directory where it extracted its content and then just copy all or just the profile you want to the "Color" settings directory, should be /home/YOUR_NAME/.local/share/icc (be sure to enable hidden folders from the "View" menu at the top). Finally open up "Color", add profile and in the window that opens you'll see all the profiles you placed in the directory. Hope that helps. ;-)