Here, we separate the integral part and fractional part.

$$\begin{gathered} =\left(5+6+7\right)+\left(\frac{1}{4}+\frac{2}{3}+\frac{1}{6}\right) \\ =\left(18\right)+\left(\frac{3+4\times 2+2}{12}\right) \\ =18+\frac{13}{12} \\ =18+1\frac{1}{12}=19\frac{1}{12} \end{gathered}$$

Hence, Option E is correct.