Help!!! My kitchen sink is some synthetic material so I do not want to use anything abrasive. It has grown a dirty film on the sides. For some reason the bottom is clean and there are some clean spots on the sides in stark contrast to the mineral deposits surrounding them.
I wish I knew what made those spots so clean. I have tried full-strength Zep calcium and stain remover. Spit would have worked just as well. Vinegar, Kaboom, and other cleaners have been just as ineffective. I even tried steam cleaning with zero results.
Every time I cleaned my sink in the past I always included the sides so I don't know why they look different from the bottom. My sink is mocking me.

Suggestions that don't include replacing the tiled-in, flush-mount sink?