ADT wants me to pay for a cancelled contract

I cancelled my month to month contract with ADT in May 2021 due to poor response - this happened several times, there were issues every month. Now I’m being asked to pay for services rendered in June whereas by then the ADT radio was already disconnected and I had signed with another service provider and I had no use of ADT services whatsoever? When I signed up I was told all I had to do on cancellation was to inform ADT in writing, which is exactly what I did. I will not pay for services I did not use. ADT customer services wanted to escalate the matter and even offered me a cheaper rate but I was already so fed up by then, you cannot retain a client when you cannot offer services to the client’s satisfaction. Their response team had recently told my daughter to go outside after 10pm to check what was happening and I just knew this was not the kind of service I wanted to pay for. Now they want me to pay for services for June which I did not even use, exactly what am I paying for when they could not even provide response when I was paying?