Damage and HOA common property - who is responsible?

For several years I have had issues with my bathroom toilets backing up dues to the roots of huge oaks trees that are on HOA common ground interfering with the sewer line to my home. I have had the line snaked and cleaned out. A crack was caused by the roots and the roots got into the line. The damage is on my side of the property which needs to be repaired by going under the the sidewalk and is costly.This was caused by trees on common ground. The HOA group of appointed home owners in the community feel that it is my responsibility to pay for the damages. They refuse to cut back trees or even maintain the trees much less pay for the damages caused by roots. Are they liable? Thank you for your help.  

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