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$\large |x - 1| + |2x-1| + |3x-1| + \cdots + |300x-1|$

If the minimum value of the expression above is $\dfrac AB$, and it occurs when $x = \dfrac CD$, where $(A, B)$ and $(C, D)$ are each coprime pairs of positive integers, find $A+B+C+D$.

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