2021 Pascal Problem 20

Three cubes have edge lengths 3 cm, 12 cm, and x cm. The average volume of the three cubes is 700 cm^3. The value of x, rounded to the nearest integer, is

\textbf{(A)}\ 6\quad \textbf{(B)}\ 10\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 7

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.