When you have run a main line cable down your drain and it is still backing up, it is time for a camera inspection. Many times when people rent sewer and drain cleaning equipment, they break through the clog, but don't remove all of the roots. It takes an experienced technician to do a thorough job. The roots simply grow back again or fall back into place because they were just moved aside by the cleaning equipment and not cut out. Pipes need to have all of the roots scraped off of the full interior diameter of the pipe and pushed out to the sewer main. It is possible that the city sewer is backing up but not as likely as what I've described above. In addition, if you have roots in your piping, I would have a professional run a video inspection camera down your line and the two of you can examine the condition of the piping by looking at the video monitor. Many people resist paying the extra money for the camera inspection, but you will learn the exact condition of the piping, any damage caused by roots and how much longer your pipes will last. Just remember the sewer line in your yard is your responsibility, it doesn't belong to the city.
A camera inspection will show you if the problem is inside the house or out in the yard. The camera will also measure the distance between clean-outs and even locate missing clean-outs you didn't know were there. With a camera, you can see the vertical riser for a clean-out coming off the pipe and locate it exactly with the radio transmitter on the end of the camera head.