We have a vinyl sheet floor in our kitchen that was in good shape when we moved in, but had been somewhat difficult to keep clean. When Roxas, our cat, got fleas in 2010, Orkin came to spray the house and the floors were never the same. We never saw a flea again, but our floors collected dirt that didn't want to come off. It was so uniform that it looked simply like a darker version of our original floor. After trying many things, I somehow came across vinyl floor stripper by Armstrong. The difference, though hard to determine in a photograph, was like night and day.
It looks like a shadow, but that was the layer of dirt on the floor. The process was a bit messy, but not difficult. The product is poured on the floor, you let it sit, then scrub it, then wipe it up. All the dirt and reside come with it. It's much easier with two people, but you could manage it by yourself. Aaron and I finished our kitchen in a couple hours, then reapplied a protective finish.