Trash in Bali is not specific to Jimbaran but all beach locals.
In my opinion having visited Bali since the early 1980s: Bali has ALWAYS had "trash" on the beach. Why? Locals have ALWAYS made their religious offerings directly into the sea water. The offerings are composed of food, flowers, and other items of gift to the gods. The local feral dogs and monkeys used to take care of it. Still Bali has never been a really great beach local in my opinion.
So what happened to Bali that made it worse? Plastic bags. The bags originally were often black and white striped. You could see them all over the beaches. Prior to plastic the locals had used banana leaves for transporting and containing goods. Those banana leaves when discarded were simply dropped haphazardly when they were finished use. Then of course so were plastic bags tossed without care. The change from organic to plastic happened really fast. Locals and some visitors never seemed to get the hang of dealing with the garbage. They were not accustomed to not naturally composting. Habits are hard to change. Bali changed to dramatically so fast it is paying the cost now. I could go on and on but think this is enough
Don't blame the IC resort for systemic island issues. Sure it would be nice if they cleaned it but there is just so much debris. Who knows if it is possible to keep up with the trash?
Do visit Bali for the culture not primarily sitting on the beach.