Looks very much like wire turf algae which fits your description well. This stuff is slimy, course and wire like which is impossible to pull off and just keeps sprouting at will. Its a battle to both control and remove but not impossible.
It is best dealt with in a separate container of tank water outside of the tank to encourage reproduction and a trick that works at times to to press it done with your fingers and then pull it off in a sheet/section.
If this does not work, soaking in fluconazole (flux), peroxide or liquid vibrant will help to loosen.
After clean up, cleaners that will help clean the rest are : Emerald crabs (which I rarely trust), chiton snails, ninja star snails and pencil or pin cushion urchins.
Reducing white intensity will also help weaken root system.