Hot water coming out of cold

I have a Price Pfister shower faucet, it is a single lever turn handle type. When I turn it to the cold water setting I get hot water for the first few minutes. It then goes cold but it is very hard to regulate warm water, I either get hot or cold. I was assuming it is a valve within the cartridge that separates the hot and cold. I am also getting hot water coming out of the sink tap for about 30 seconds now as well. Will replacing the cartridge in the shower faucet solve both problems or is something else going on with the plumbing?

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