Solve 21.55 + 216 - 13.515 = \ ( ? )^1/34 \ + 1730

Answer: Option E

Let the missing number be x
$$\begin{array}{rl}& \frac{21.5}{5}+\frac{21}{6}-\frac{13.5}{15}=\frac{{\left(x\right)}^{\frac{1}{3}}}{4}+\frac{17}{30}\\ & \frac{21.5}{5}+\frac{21}{6}-\frac{13.5}{15}-\frac{17}{30}=\frac{{\left(x\right)}^{\frac{1}{3}}}{4}\end{array}$$
L.C.M of 5, 6, 15 and 30 is 30
$$\begin{array}{rl}& \frac{129+105-27-17}{30}=\frac{{\left(x\right)}^{\frac{1}{3}}}{4}\\ & \text{root}3\text{of}x=\frac{190\times 4}{30}\\ & \text{root}3\text{of}x=25.33\approx 25\\ & x=25^3\\ & x=15625\end{array}$$
Hence, the numbers 15625