How are both integers

The sum of absolute values of all real numbers \(x\), such that both of the fractions \(\frac{x^2+4x-1}{7x^2-6x-5}\) and \(\frac{1-x}{1+x}\) are integers, can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

Details and assumptions

If you think that there are no real numbers \(x\), then the (empty) sum is 0, and you should type your numerical answer as 1.

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