I don't recognize the valve from your description. You could make a drawing of it or take a photo and show it to a clerk at a plumbing store. Or look at valve cartridges at a home center to see if you recognize it.
A Moen valve would have a small retainer clip at the front. Obviously, turn off the water and then pry up on the clip to remove it. Be careful not to drop it down the drain! Then the cartridge will come out, although probably not easily.