The private certificated pilot was departing toward the east from a remote airstrip on a Title 14, CFR Part 91, local area flight. The airstrip was about 600 feet long and about 15 feet wide. During the takeoff roll, the pilot reported that the airplane's left main landing gear tire encountered soft conditions along the left edge of the airstrip. The airplane pulled to the left and departed the left edge of the airstrip, collided with high brush, and overturned. The airplane received structural damage to the left wing spar and the right wing lift strut.