If I gave my notice to move out of my apartment on time but management says that they did not receive it, what do I do?

Question Details:

My apartment complex require 60-day notice to move out. I gave handwritten notice on time in July. I took it to the office myself. I received a notice yesterday stating that I did not give timely notice and that I would either have to incur month-to-month rate at double the rent, or renew my lease. I don't have the money to do either, that's why I am moving. What can I do?

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