It depends on the clauses contained in your lease agreement. Are you breaching the lease by moving out before the end of the term of the lease?
Depending on what your lease says, unless you are going to completely clear the premises by the 6th, than you will likely owe rent for as long as you live there and/ or have your possessions in the place. All your notice does, is it gives the landlord a heads up that you intend on moving out, so they can find a replacement tenant for your place, it does not relieve you of paying the rent for next 30 days.
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