The pilot reported that during the landing and rollout, the airplane was going faster than he wanted at his normal turnoff point on the runway so he continued to the next turnoff. While turning, he applied the brakes, raised the flaps, and pushed in the carburetor heat control. At that time, he realized that the airplane was not stopping so he applied more braking, but the airplane did not slow down or stop. Before he could move his feet higher onto the toe brakes, the airplane departed the runway surface onto bumpy ground, headed over a bank, and nosed over. The wings, vertical stabilizer and rudder were substantially damaged. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.