A mutation for having a higher radiation resistance or higher resistance to cancer is something that already happens in nature, but in most of the animal world those are relatively useless traits, normally cancer doesn't develop fast enough to stop procreation.

In Chernobyl, the highly elevated radiation would normally kill animals before they can even breed. The ones that don't have the resistance die before they get the chance, the ones that do have a higher resistance breed.

With humans in the modern age, a resistance to cancer or radiation trait never gets the chance to become a dominant evolutionary trait as most all people only develop the cancer later in life and the ones that do get cancer early more and more often can get treatment giving them a chance to procreate even when they got cancer young.

Outside Chernobyl, there is no evolutionary pressure for a trait like that to become dominant.

Living long enough to procreate is the primary drive in nature.

We generally don't see fast evolutionary changes in nature because nature doesn't change quickly often.

Leave it to us, humans, to create situations where the change is drastic and quick.