21.5/5 + 2 1/6 - 13.5/15 = ( (?)^1/34 ) + 17/30

Answer: Option C

$$\begin{array}{rl}& 2\frac{1.5}{5}+2\frac{1}{6}-1\frac{3.5}{15}=\frac{x^{\frac{1}{3}}}{4}+1\frac{7}{30}\\ & \Rightarrow \frac{11.5}{5}+\frac{13}{6}-\frac{18.5}{15}=\frac{x^{\frac{1}{3}}}{4}+\frac{37}{30}\end{array}$$
⇒ L.C.M. of 5, 6 and 15 is 30
$$\begin{array}{rl}& \Rightarrow \frac{69+65-37}{30}=\frac{x^{\frac{1}{3}}}{4}+\frac{37}{30}\\ & \Rightarrow \frac{97}{30}=\frac{x^{\frac{1}{3}}}{4}+\frac{37}{30}\\ & \Rightarrow \frac{x^{\frac{1}{3}}}{4}=\frac{97}{30}-\frac{37}{30}\\ & \Rightarrow x^{\frac{1}{3}}=\frac{60}{30}\times 4\\ & \Rightarrow x^{\frac{1}{3}}=8\\ & \Rightarrow x={\left(8\right)}^3\\ & \Rightarrow x=512\end{array}$$
Hence, the number is 512