Solve $$\frac{{21.5}}{5} + \frac{{21}}{6}$$ $$ - \frac{{13.5}}{{15}}$$ $$ = \left\{ {\frac{{{{\left( ? \right)}^{\frac{1}{3}}}}}{4}} \right\}$$  $$ + \frac{{17}}{{30}}$$

Solution(By Examveda Team)

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