How can I unclog a toilet that is clogged due to non-toilet paper?
If the soap doesn't work, I'd go with a drain zip before going to a snake.
There are a lot of brands, burt basically a drain zip is a three dollar, 2.5 foot (3/4 meter) long flat, bendy piece of plastic, with plastic barbs along the sides. It's great for getting hairballs out of the shower drain, and should bend its way quite nicely through the toilet to the point of your blockage. Most hardware stores (US) sell the things.