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Algebra Level 5

The real number answer to the equation \(x^3 = x+1\) is \[x = \sqrt[3]{\frac{1}{2}+\sqrt{\frac{j}{k}}}+\sqrt[3]{\frac{1}{2}-\sqrt{\frac{j}{k}}}\] for positive integer \(j, k\) being relative prime. Find \(\sqrt{16+jk}\)

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