Can you support a 20ft 2x6 only at the ends?
2x6 DF #2 Supported o the ends can handle about 11 lb. per Ln. Ft. total load.  This would include snow.  would recommend at least 2x8 if you are okay with sagging from wood creep after many years.  4x8, (2) 2x8, or 2x10 would be better.