Thanks for all the helpful replies.
I started with a large plunger. Open the flush valve and push. On the first push I heard a bang come from below the toilet but no drainage. I repeated the plunging for about 10 times. No drainage. I got a short snake with a long handle. It felt like I couldn't touch bottom with it. So I went back and got a 15' snake. It went all the way in, but I think it was curling up. Still no drainage. I went up on the roof and checked the vents. They're both open.
Could I use something like Drano on it? Would that hurt the system?
I tried the broom handle again and it goes 18" (measured) before hit something. How do you find the tank outlet?