Jet/Whirlpool Tub Black Particles

Hello All, Recently purchased house that has a jet tub with 6 jets in it in the bathroom. Filled up with water to test and noticed a surge of black crud and particles being emitted from the jets. Was told dishwashing detergent might help so I tried running it for 15-20 with that and still spits the dirt out. Since then have tried dishwasher detergent (powder aka Cascade), bleach and even drove an hour to the spa and pool place and purchsed a spa cleaning kit for $20. Followed that according to directions and still have black particles coming out, but considerably less than the first time I ran it. My question is: Is there any tricks or hints to rid this, or will it never be completely black particle free? Thanks as this is the first time I ever dealt with one of these.

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