Have a separate garbage bag for when you come. Leave his to build up and continue disposing of yours. After a couple days of pile up, either:
A) He’ll get the msg that you are not his garbage collector and you do not agree to be stepped on. (if he is purposely doing this)
B) The manager will confront you and you will respectfully let him know that you do remove your garbage and are too annoyed with the lack of cleanliness due to Dan.
Or you can just take the high road though not recommendable if it will cause you a frustration build up.