To solve this equation, we first need to simplify both sides of the equation.

On the left side:
(-4x)^3 = -4x -4x -4x = 64x^3

On the right side:
27(1/3)^3x = 27 (1/27)^x = 27 1 = 27

So the equation simplifies to:
64x^3 = 27

To solve for x, we need to find the cube root of both sides:
x = ∛(27/64)
x = ∛(27)/∛(64)
x = 3/4

Therefore, the solution to the equation is x = 3/4.