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Yes, the trash company could be held responsible. It depends on a lot more facts than what you have provided, but basically it is as you said, they may not have known the septic tank was there but a reasonable person should know that driving a truck on to someone's yard would cause damage.
You should pay a visit to a few different attorneys who specialize in automobile accidents. Any good attorney who practices in this area will give you a free consultation, and will be able to tell you based on all of the facts whether or not you have a case.