\[\frac{3}{7} + \frac{1}{6} + \frac{5}{6} + \frac{6}{7} = \frac{9}{7} + \frac{6}{6} =\]
\[= \left( \frac{3}{7} + \frac{6}{7} \right) + \left( \frac{1}{6} + \frac{5}{6} \right) =\]
\[= 1\frac{2}{7} + 1 = 2\frac{2}{7}\]