To solve for x, we can start by isolating the x term on one side of the equation:

27x^3 = -1

Next, we can divide both sides by 27 to solve for x:

x^3 = -1/27

Taking the cube root of both sides:

x = -1/3

Therefore, the solution to the equation 27x^3 + 1 = 0 is x = -1/3.