# A function from dice

Consider a function $$f(x)=x^3+ax^2+bx+c$$, where $$a, b$$ and $$c$$ are chosen respectively by throwing a dice thrice. If the probability of $$f(x)$$ is an increasing function can be represented by $$\dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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