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To solve this equation, we can first rewrite it as:

3^(1/3) * (10 - x)^(1/3) - 3^(1/3) * (3 - x)^(1/3) = 1

Let's denote y = (10 - x)^(1/3) and z = (3 - x)^(1/3), so the equation becomes:

3^(1/3) * y - 3^(1/3) * z = 1

Now, we can square both sides of the equation to eliminate the square root:

(3^(1/3) * y - 3^(1/3) * z)^2 = 1^2 3^(2/3) * y^2 - 2 * 3^(1/3) * y * 3^(1/3) * z + 3^(2/3) * z^2 = 1

Simplify the equation:

3^(2/3) * y^2 - 2 * 3^(2/3) * y * z + 3^(2/3) * z^2 = 1

Now, substitute y and z back in terms of x:

3^(2/3) * (10 - x)^(2/3) - 2 * 3^(2/3) * (10 - x)^(1/3) * (3 - x)^(1/3) + 3^(2/3) * (3 - x)^(2/3) = 1

This equation can be further simplified and solved by expanding the terms and isolating x.