To find the value of x that satisfies the equation (x+3)³ = 1, we first need to simplify the left side of the equation by expanding the cube of (x+3):

(x+3)³ = (x+3)(x+3)(x+3)
= (x+3)(x² + 6x + 9)
= x³ + 9x² + 18x + 9

Now, we have the equation:

x³ + 9x² + 18x + 9 = 1

Simplify further:

x³ + 9x² + 18x + 9 - 1 = 0
x³ + 9x² + 18x + 8 = 0

The next step is to solve the cubic equation. It may not have a simple solution, and finding the exact root may involve using numerical methods or calculators. Alternatively, the equation can be manipulated further to try and factorize it into simpler expressions.