HMMT November 2011 T3

Find the sum of the coefficients of the polynomial $P(x)=x^{4}-29 x^{3}+a x^{2}+b x+c$ , given that $P(5)=11, P(11)=17$ , and $P(17)=23$ .

Dataset text NuminaMath olympiads. Quoted with source.

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