From \(\dfrac{5a+7b}{6a+5b}=\dfrac{29}{28}\)we have:

\(29\left(6a+5b\right)=28\left(5a+7b\right)\)

\(\Rightarrow174a+145b=140a+196b\)

\(\Rightarrow34a=51b\)

\(\Rightarrow2a=3b\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{3}{2}\)

\(\Rightarrow a=3k;b=2k\)

Because GCM(a,b)=1 so k=1. That means a=3, b=2.