It depends on the employment rules of the State where you work and if the contract is enforceable. An attorney would need to review the contract to answer your question.
Normally the law requires that parties to a contract follow the terms of the contract. Perhaps the bigger question is what are the penalties under the contract?
No one can answer your question without reading the entire contract. You may quit without giving the 60 day notice, but there could be damages payable as a result of your breach of this contract. A better solution might be to go to the employer and obtain a waiver of this provision, and negotiate a shorter notice period.
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