Well..there are two public beach areas - one by the community center (which is what I believe you are referring to) as well as Long Bay Park which is north, close to the All Inclusives.
Both are kept relatively in shape in my opinion for what they have to work with.
There is one or two organized beach clean up days during the year.
BUT...anytime I am at the beach be it in Negril or here in Northern California if I see litter or cigarette butts lying around I pick them up. I think a lot of people do that. When we used to go to Little Bloody Bay, which was completely undeveloped and un-touched by anyone our first moments there were usually spent raking up the trash that the RIU employees would leave around from their lunch, collecting that which we could not burn to carry out with us and burning the burnable stuff.
Its important that we each take responsibility for our environment, even if it is on a beach that we think is maintained. This way everyone can enjoy it for years to come.