Longest side is in interval

Geometry Level pending

If \(a\), \(b\), and \(c\) are three sides of a triangle, then the value of \(\max (a,b,c)\) is in the interval \([p(a+b+c),q(a+b+c))\). If \(p+q\) can be expressed as \(\dfrac{x}{y}\), where \(x\) and \(y\) are relative primes, find \(x+y\).

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