I have had this exact problem. Double kitchen island sink. P trap on 1 side. Garbage disposal & P trap on the other. Both drains converge into 1. The piping under the sink looks like an upside down "U". The right side drains down to the septic and is where the double sink drains are connected. The left side is the vent. Both sides have a 1 3/4" clean out screw cap. Obviously, the right clean out cap will leak water when removed but covering it with my hand a bit allows the drain to work well (just like venting...). The left vent side, when opened, allows the drain to drain quickly and easily. When I replace the cap, the drain gurgles like pouring soda from a 2 liter bottle. I snaked back 30 feet numerous times. Only the first time did I clear a clog... onion skins and grease but not enough to clog the drain so much as to stop it from draining. The gurgle always remained. I climbed onto the roof, snaked the vent to the first "resistance" (about 10 feet or so) and pulled out a rotted mass of dead sparrow and small pieces of leaves. I then continued the length of the snake. The kitchen sink has drained better then ever. No issue since.
I don't understand why several people don't understand the basics of plumbing. Venting is a must! Sure a pipe will drain from source to septic but it will only drain as air passes the mass of liquid to equalize the pressure to "outside air". AGAIN--- ONLY will drain as the air pressure is equalized. Like the straw analogy - plug 1 end and it holds water, remove your finger or cut a small slit in the middle of the straw and the water pours out. When a vent is in place, allowing the air to equalize, the fluid in the drain will drain with ease. The vent prevents water suction. This is also why you may have to use a plunger to unclog your toilet. You are moving to the clog and forcing air to equalize the pressure since the clog usually happens before the water trap.
I'm certain that there are more involved issues out there but this simple fix was completed in an hour and the vent now has a weather-proofed cover.