Zeolite...
Is listed on there salt packets, and from my limited tasting, they seem do be, actually, really salty goodness
Anyhow, typically, water softening products, (like White King ) contain, strong Builder Agents, and these agents will actually pull calcium and magnesium deposits, out of clothing. Clothes, really do look much better when washed in Soft Water, or Softened water, because those Calcium Deposits, actually work against, and bind with your detergent, and they get all trapped in the fibers, giving you that nasty dingy look.
Everyone seems to think, Clorox is the answer, but when it reacts to Hard Water, you get that pastel Yellow look. I think for you, the White King, or another packaged water softener product, is going to give you the best results.