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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