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You could replace, but you may first want to try this:
Whether at your present Dentist or a new one, they could use something called "finishing strips" to use to make food catch less & hopefully not at all - with regards ***** ***** the teeth. It would likely help. And the mucky stuff on the back of the right tooth? Tell the Dentist about it. It sounds like perhaps some excess cement may well be stuck there (incidentally of course), which could & should be polished off easily.
Best of all, none of the above requires any numbing, and shouldn't take more than 10-15 minutes. There's a good chance it may do the trick!
I'll be gone for a couple hours. Please "DO" right back if questions - I'll check upon my return - OK?
Best wishes to you!
Does the above makes sense?