CD player cleaning discs, do they work?

Do you think cleaning discs for CD players work? I've got one that I used a couple of years ago for my car's CD player, but the player broke shortly after I used it. Made me suspicious.

My current CD player acted a little funny this morning (showed the track but didn't catch) and then worked well this evening. Not sure that I want to try cleaning it, since, coincidence or not, the previous one broke last time I did that.
CD player cleaning discs, do they work?
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