To solve the equation, we can take the cube root of both sides:

∛((91 - x)^3) = ∛64

Simplifying the left side:

91 - x = 4

Now, we can isolate x by subtracting 91 from both sides:

-x = 4 - 91

Simplifying:

-x = -87

Finally, we can solve for x by multiplying both sides by -1:

x = 87

Therefore, the solution to the equation is x = 87.