In this context, the word "sum" is usually associated with arithmetic, like amounts of money. The word "total" has a more general use. The total is derived from adding together smaller amounts. In the example you mention, the word "sum" could be used, but it sounds a bit strange.

Usually we use "sum" when we talk about money it means "an amount of money" and when the mathematical operation of adding is implied e.g. "the sum of 6 and 7 is 13", but we use "total" when we mean the final number of things or people.

The two can be used interchangeably. The usage though would greatly depend on what is more suited to the context of the sentence. In my opinion, "total" is more suitable than "sum" for the sentence that you constructed.