time
If the sewer is flowing so the material just goes past the roots and down the drain, then it could take forever. If the roots have the drain line completely closed so the drain is completely plugged, it will also take forever. In between those two situations it depends on how long the roots stay in contact with the material so they can absorb it. AND then they have to die and rot away before it becomes effective. Hopefully when they rot away they do it in stages. If it all happens at once the mass will plug your sewer and you will be back where you started, calling a plumber.