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Yes. You will be able to break the lease as this is what is known as a constructive eviction (especially if you have complained to the property management company/owner and they have done nothing to fix it). The only issue I see that hurts your case is that you actually moved into the unit despite it's condition. You should have tried to break the lease once you saw the condition the unit was in and not have moved in.
You will not be able to recover anxiety and mental anguish. However, any money spent on the move, rent, etc. would be recoverable.
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