55.1+1 6767.

$$5 \frac{5}{6} \cdot 1 \frac{5}{7} + 1 \frac{1}{6} \cdot \frac{3}{7} = \frac{5 \cdot 6 + 5}{6} \cdot \frac{1 \cdot 7 + 5}{7} + \frac{1 \cdot 6 + 1}{6} \cdot \frac{3}{7} = \frac{30 + 5}{6} \cdot \frac{7+5}{7} + \frac{6+1}{6} \cdot \frac{3}{7} = \frac{35}{6} \cdot \frac{12}{7} + \frac{7}{6} \cdot \frac{3}{7} = \frac{5 \cdot 2}{1} + \frac{1}{2} \cdot \frac{1}{1} = 10 + \frac{1}{2} = 10 \frac{1}{2} $$

Ответ: $$10 \frac{1}{2}$$