When the graph of \(\frac{{{y}^{2}}}{x}\) against \(\ln x\) is drawn, a straight line of \(\ln x=\frac{{{y}^{2}}}{kx}+\frac{n}{3}\) is obtained. Given that this line passes through the point \(\left( 2,5 \right)\) and has a gradient \(3\), find the values of \(k\) and \(n\).
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