Please reason step by step, and put your final answer within \boxed{}.
Let \( C \) be the curve \( y^2 = x^3 \) (where \( x \) takes all non-negative real values). Let \( O \) be the origin, and \( A \) be the point where the gradient is 1. Find the length of the curve from \( O \) to \( A \).
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