Drain gurgling due to blocked sewer pipe?
Gurgling is caused by a partial blockage of either the sewer or the vent.  This blockage could be in the main sewer pipe leaving your house, or anywhere in the waste pipes of your house.  Likewise with the venting.

Without finding where the blockage is, you cannot say with any certainty that the belly in your sewer is the problem.  Video inspection is probably a good idea in your case.