The function \(f\) defined by \(f(x)= \frac{ax+b}{cx+d}\), where \(a\),\(b\),\(c\) and \(d\) are nonzero real numbers, has the properties \(f(19)=19\), \(f(97)=97\) and \(f(f(x))=x\) for all values except \(\frac{-d}{c}\). Find the unique number that is not in the range of \(f\).

(第十五届AIME1997 第12题)