Given points \(P(-1,-2)\) and \(Q(4,2)\) in the \(xy\)-plane; point \(R(1,m)\) is taken so that \(PR+RQ\) is a minimum. The original answer is in the form \(-\frac{a}{b}\), where a and b are integers and the fraction is in its simplest form. Please find the value of \(a + b\).

Let's think step by step and output the final answer within \boxed{}.
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