Notice of termination has to be given in writing. Voicemail is not good enough, no need for the LL to call you back if the procedure is clearly outlined in your lease. If you gave written notice on October 20th--Dec 20 would be the date of termination. No unjust enrichment--you have the property until Dec 20th and you have to pay up to Dec 20th.
Landlord MAY allow you out of the contract earlier than Dec 20th--perhaps with a fee, perhaps if you can line up a suitable tenant to replace you--they will waive the fee or waive any legal action against you---it may require some creative negotiation, and the LL is not obligated to make a deal, but it can be done.
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