They call it logarithms?

Algebra Level 5

\[\large \log_{\frac{3x}{x^2+1}} \left(x^2-\frac{5}{2}x+1\right) \geq 0\]

If the range of \(x\) satisfying the above inequality is in the form \( (a,b) \cup [c,d)\), then find \(a+b+c+d\) where \(a,b,c,d \in \mathbb{R}\).

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