Thats an incredibly marxian view, I think you would need to define what you mean by "working class" and "Upper class"

Although it is a perfectly reasonable question, we don't have texts from this early so we are forced to make educated guesses using archeology to answer these sorts of questions. While archeology is pretty good at providing a general picture of the material conditions of different times and places, it doesn't have the kind of specificity you are looking for with a question like this. We can say with relative certainty that most people living in ancient Sumer were farmers, that they worked irrigated fields using various types of plows, animals, and tools, but we have no idea if they worked every morning and afternoon or if they took a siesta, if they were specialized in different tasks of the field or if they were generalists.

We do have texts from about 3200 BCE, but it will be another thousand years before we have anything resembling enough detail to answer this question with any detailed specifics. A close reading of the early literature can give us clues, but it is nearly impossible to determine how common the things the clues reveal may have been.

Whole books have been written on this question about Mesopotamian societies in general, but few deal with this ultra-early period in your question. For daily life in the ancient Near East in general, I recommend Life in the Ancient Near East, 3100-332 B.C.E. by Daniel Snell.

Feel free to ask the question again with more specificity and a later time period if you want more detailed information.