REQ: Bathtub Repair Tips

I have a one year old bathtub, a regular type. Right before the drain fixture, there is a crack. a crack that was caused by a falling object. This crack is more of a "peeled off ceramic coating". It is deep enough to let the water go in and flood my kitchen below. I tried to patch it with a silicon type sealant but after a few wash, it came off easily.
Please give me some advice on how to repair the crack permanently. Is there a sealant that is strong enough to stay for years? Can I just simply apply a gout?
I would appreciate any advice you can share. Thanks in advance.
Regards, Giggle

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