Have chronic slow laundry drain. Original root problems corrected with new line to street. 20 ft snake helped some but drain is still too slow.

How well is the line vented? If its not enough then that could be your problem.

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20 ft snake helped some but drain is still too slow.

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Perhaps you need a longer snake.
Is your complaint that it drains too slow or does it back up out of the stand pipe? How old is your house? What size trap and stand pipe do you have? Back to you, Tom