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A polynomial with integer coefficients P(x)=amxm+am−1xm−1+⋯+a0P(x)=a_{m}x^{m}+a_{m-1}x^{m-1}+\cdots+a_{0}P(x)=amxm+am−1xm−1+⋯+a0, with ama_{m} am and a0a_{0}a0 being positive integers, has one of the roots 23\frac{2}{3}32. Find the nthn^\text{th}nth smallest (n≥10)(n \geq 10)(n≥10) possible value of a0+ama_{0}+a_{m}a0+am.
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