You have to provide evidence

that there were no crack on your tooth before whiting. You also have to read the documents you signed before the procedure. Usually the dentist will let you sign the documents showing that he will not be responsible for any damage or accident that beyond his control. If he had followed the standard procedure and made no mistake in your whiting you will had a VERY difficult time to get 索賠 from court. However, You can complain to him and to let him reduce the cost of the procedure by giving him impression that if he doesn't, you may file complains to the association that regulates the dentists. But sucessful rate is tame.