An airline transport pilot was departing a private grass field in a special light sport airplane with a passenger onboard. With calm wind, the airplane began a takeoff roll to the west on an approximately 1000-foot-long turf runway. The pilot said that during the takeoff roll the airplane encountered a dip/bump in the runway, which reduced groundspeed and extended the ground roll. The airplane became airborne near the end of the runway, where it started to lose lift and struck an unseen wire with the right main landing gear. The wire was a solar/electrical wire, at a height of approximately 1 to 2 feet, which ran along an adjacent soybean patch. The airplane's nose then pitched down and the airplane came to rest at the bottom of a 5-foot embankment. The pilot reported that due to the density altitude and the weight of the airplane, he could not gain sufficient airspeed during the takeoff to climb. The pilot added that had the unseen wire not "snagged" the landing gear, the airplane would have been able to continue accelerating and climbing. The airplane received damage to the propeller, left leading edge of the left wing, the landing gear, and the fuselage. The pilot reported no preaccident mechanical deficiencies or mechanical problems with the airplane.