\(1 \frac{5}{6} +2 \frac{2}{11} =\frac{(1\times6)+5}{6} +\frac{(2\times 11)+2}{11} =\frac{11}{6}+\frac{24}{11} \\\\=\frac{11\times 11}{6\times 11} +\frac{24\times6}{11\times6} =\frac{121}{66} +\frac{144}{66}=\frac{121+144}{66} =\frac{265}{66}\\\\=\boxed{\bf{4\frac{1}{66}}}\)
