2025 Fermat Problem 24

Suppose that f(x) = x^4 + px^3 + qx^2 + rx + s for some real numbers p, q, r, s. In addition, f(1) = 59, f(2) = 118 and f(3) = 177. If T = f(9) + f(-5), what is the sum of the digits of the integer equal to T?

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