If your trash overlay shows any red bars of trash, then you have a true trash problem. If they're protesting at city hall about garbage but everything is picked up, it's possible you had a problem that's been fixed now and they will eventually stop the protest. Most of the time a trash issue is because of traffic or not enough incinerators or dumps to keep up with the trash. Since your neighboring city is providing all of the trash service, make certain that the garbage trucks are able to get in and out of your city. If they're stuck in traffic at the entrance they may not be able to pick up all the trash by the time they get in. If it takes until the end of the day for them to get into the city, they will just turn around and leave.
I'm a little confused that you say all trash is being picked up but that your trash level is "415 of 1318 and recycle is 6309 of 108,134". Time of (Sim) day is probably the reason. The garbage trucks go out in the morning and will run through the city all day long to pick up the trash. As long as they have picked up everything by the end of the day, it's fine. But if they can't get to all the buildings during their work day, the trash will pile up and overflow, causing garbage problems. Watch your trash overlay for a Sim day, and see how long it takes for the trucks to arrive and get through your city and back out. Check the numbers at 8 pm, they should show all of the garbage picked up by then.
There is another possibility, the garbage trucks from the region may have gotten lost or disappeared (again, this usually happens when they can't get to their destination in time due to traffic issues). The city providing the garbage service should try demolishing the truck garages and rebuilding them, that will put new trucks in. Also, they need to have the capacity to deal with all the trash - enough dumps to hold the garbage, and enough incinerators to process it so there is none remaining by the time the next day's collection starts.
If I were you, I would put in a garbage dump in your city in an out-of-the-way place, and let each city take care of its own garbage. Keep an eye on your traffic issues and make sure the trucks can get through the collection by the end of the day, and process the garbage by the beginning of the next day. Once it's all caught up and your traffic issues are solved, you can always demolish it.