technology I've accidentally damaged a DVD and a Blu-Ray that I own

[Nightfall Gloam 18,266]

Pretty much as the title and tags say. I've recently been panicking about the integrity of some of my DVD's because I've placed them in a cupboard in a usually pretty high temperature (because of heating) room in my house, and for some reason, it got me to the point where I tried to clean one of my DVDs because of one tiny dust particle that wouldn't even affect playability, and it ended up scratching the disc. Anyway, I heard that you can apparently clean scratches off of DVDs with toothpaste and a soft cloth and I wanted to know if anyone has tried this method and if it works (as well as if it can work on Blu-Rays/HD DVDs without damaging the disc(s) further, and any further advice you may have)