A polynomial with integer coefficients \(P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}\), with \(a_{n} \) and \(a_{0}\) being coprime positive integers, has one of the roots \(\dfrac{2}{3}\). Find the **third smallest** possible value of \(a_{0}+a_{n}\).

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