\(\frac{5}{6}+6\frac{5}{6}\left(11\frac{5}{20}-9\frac{1}{4}\right)\)
\(=\frac{5}{6}+\frac{41}{6}\left(\frac{45}{4}-\frac{37}{4}\right)\)
\(=\frac{5}{6}+\frac{41}{6}.2\)
\(=\frac{5}{6}+\frac{41}{3}\)
\(=\frac{5}{6}+\frac{82}{6}\)
\(=\frac{87}{6}=\frac{29}{2}\)