-10 2/7 + 1 13/35 + 3 9/11 ÷ 1 1/55

To add the mixed numbers, we first convert all fractions to have the same denominator. The least common multiple of 7, 35, and 11 is 385.

-10 2/7 = -10 110/385
1 13/35 = 1 55/385
3 9/11 = 3 105/385
1 1/55 = 1 7/385

Now we add the mixed numbers:

-10 110/385

-5 253/385

Therefore, the result is -5 253/385.