Fun with Simplifying Fractions

The number of integers \(x\) with \(-2014 \le x \le 2014\) for which the fraction \(\dfrac{x^2+2014}{x^2+2017}\) is already in simplest form can be expressed as \(1000a+100b+10c+d\), where \(a\), \(b\), \(c\), and \(d\) are (not necessarily) distinct integers from \(0\) to \(9\), inclusive. Find the value of \(a+b+cd\).

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