[tex]\displaystyle\\
(-1)^{6}+\frac{7}{3}\left(\frac{1}{7}-\frac{2}{25}:\frac{7}{5}\right)=\\\\
=1+\frac{7}{3}\left(\frac{1}{7}-\frac{2}{25}\times\frac{5}{7}\right)=\\\\
=1+\frac{7}{3}\left(\frac{1}{7}-\frac{2}{5}\times\frac{1}{7}\right)=\\\\
=1+\frac{7}{3}\left(\frac{1}{7}-\frac{2}{35}\right)=\\\\
=1+\frac{7}{3}\left(\frac{5}{35}-\frac{2}{35}\right)=\\\\
=1+\frac{7}{3}\times\frac{5-2}{35}=1+\frac{7}{3}\times\frac{3}{35}=1+\frac{1}{5}= \boxed{1\frac{1}{5}}=\boxed{\frac{6}{5}}[/tex]