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

∛((x-1/4)^3) = ∛(-27)

Simplifying the left side:

x - 1/4 = -3

Adding 1/4 to both sides:

x = -3 + 1/4

Combining like terms:

x = -12/4 + 1/4

Simplifying:

x = -11/4

Therefore, the solution to the equation is x = -11/4.