Month to Month Apartment Lease Question

Question on moving out of a month to month apartment because my apartment office is trying to charge me for a whole month because they said I need to give 30 days notice that I am leaving but I just snatched up a good home rental in less than a week that I didn't want to lose and I am moving to the rental house on the 6th. I am currently in a month to month apartment so no contract. Do I still have to pay for the whole month of April or can i get away with just paying for the days I am still here at the apartment until I am moved out at the end of this week?