Mathematics Question from JEE Main 2023 · 1 February, Shift 2

Let the sixth term in the binomial expansion of $\left( \sqrt{2^{\log_2(10 - 3^x)}} + \sqrt[5]{2^{(x-2)\log_2 3}} \right)^m,$ in the increasing powers of $2^{(x-2)\log_2 3}$, be $21$. If the binomial coefficients of the second, third, and fourth terms in the expansion are respectively the first, third, and fifth terms of an A.P., then the sum of the squares of all possible values of $x$ is _____.