The pilot took off for a training flight to a dirt strip approximately 50 miles to the east. Upon landing at the strip, the pilot decided to initiate a short/soft field takeoff down the 3,600-foot-long runway. The pilot reported that he took off with 20 degrees of flaps and was never able to get more than 10 feet off the runway surface area. At the end of the runway, the pilot noticed two 3-4 foot high dirt berms. He pulled back on the yoke, missing the first berm, but the airplane settled back down and struck the second one. The resulting impact caused the aircraft to nose over and come to a rest inverted. The airplane's pilot operating handbook (POH) states that soft or rough field takeoffs should be performed with no more than 10 degrees of flaps. Furthermore, the airport's density altitude at the time of the accident was calculated to be approximately 10,000 feet, which is 2,000 feet above the maximum altitude listed in the takeoff performance charts in the POH. The pilot reported no mechanical issues with the airplane that would have precluded normal operation.