The idea is that the unsecured creditors all get treated alike in a bankruptcy. So you have to include ALL your debts in your bankruptcy filing.
I'm not licensed in California so don't take what I say here as legal advice. It's simply information based on general principles of law which is intended to educate. If you need legal advice, please consult a lawyer who holds California licensure.
You have to list all of your debts when you file bankruptcy, whether you want to pay it or not. Keep in mind, credit card companies check your credit periodically and will cancel a card if you are in bankruptcy, whether you listed them or not. This is in addition to the fact that you are required to list all your debts and you sign your bankruptcy documents stating under penalty of perjury that they are accurate.