I have a sump pump and utility sink that tie into our main drain for the house. Every time the ump runs the sink gargles some water and then it drains. Would putting in a vent of some sort between the sink and where the ink line ties into the ump fix this?

Most likely yes. The sink actually needs a trap and vent anyway, so adding a vent would be the first logical step. Let us know how it works out.

Your sump pump shouldn't connect into the main sewer system... at least not in most states/municipalities!

Here, your sump pump should discharge to outside the home and then as MGD77 mentioned, you'd want to add a vent to the sink for best results just for the sink!

Glad to discuss more, OK?

Mark

Be interesting to see your set up.

Your sink should already be vented and if it is the vent's blocked and should be snaked. How's the sump connected to the sink? Indirect waste or a hard connection ? Mark's correct, most codes only allow sewage and gray water to enter the system, Back to you. Tom