The set of real values of \( x \) satisfying the equality \( \left[\frac{3}{x}\right]+\left[\fra...

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The set of real values of \( x \) satisfying the equality \( \left[\frac{3}{x}\right]+\left[\frac{4}{x}\right]=5 \) (where [] denotes the greatest integer function) belongs to the interval \( \left(a, \frac{b}{c}\right] \) where \( a, b, c \in N \) and \( \frac{b}{c} \) is in its lowest form. Find the value of \( a+b+c+a b c \).
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