Plumbing supply and building supply stores sell a metal tool that allows more torque to be applied. Sometimes they are just too calcified to remove and will require the fixture to be replaced. Good Luck.

(Mine was from 1972 and had to be replaced after applying so much torque that I ruined the valve, thus requiring tile and wallboard work in addition to the fixture. In the end my wife was much happier with the new installation!)

Moen has been aware of the difficulty of removing cartridges and has manufactured its own "cartridge-puller" for over 30 years. Cant remember the part # but it is a very common item. erik

Thank you both for the responses. I tried to twist it some more and the front part of the cartridge boke off. I think I have to get some professional help and probably replace the faucet.

Oh well...