Logarithmic inequality

Algebra Level 4

\[\log_{\left(\frac{x+6}{3}\right)} \left(\log_{2}\left(\dfrac{x-1}{x+2}\right)\right)>0\]

If the range of \(x\) satisfying the above inequality is in the form \((a,b)\cup (c,d)\), find \(a+b+c+d\).

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