PIMSO 2025 - Mathematics - Secondary 2 - National Round Question 11

The equation $(3-x)^3+(4-x)^3=(7-2x)^3$ has roots $x_1,x_2,x_3$. What is the value of $(x_1+x_2+x_3)$? Hint! $a^3+b^3=(a+b)^3-3ab(a+b)$.