Sewer Lines and Tree Roots

What do you do for sewer lines that are under the street with tree roots in them? I have PVC pipe for the lines on my property but where it runs into the city property (under the street) is where the clogs always are.

The city claims it is my responsibility to repair the lines that are on their property. I can't install verticle tubes to pour things into if it's a road.

Help !!!

Tim, I don't fully understand your comment about stopping the drilling when the hole is about 24" to 30" from the sewer line. If my sewer line is 36" below ground,
then this means I only drill 6" - 12" deep??

Trying to locate sewer line,city does not have records to old 1951,any sugestions on locating without costing to much money.Want to put a bathroom out back in garage. Thank you. Mark