6 1 711+3711

$$\frac{6}{7} : \frac{1}{11} + 3 \frac{7}{11} = \frac{6}{7} \cdot \frac{11}{1} + \frac{40}{11} = \frac{66}{7} + \frac{40}{11} = \frac{66 \cdot 11 + 40 \cdot 7}{77} = \frac{726 + 280}{77} = \frac{1006}{77} = 13 \frac{5}{77}$$

Ответ: $$13 \frac{5}{77}$$