The given expression is: \[ \frac{7x+1}{2}, \frac{7x+2}{3}, \frac{7x+3}{4}, \dots, \frac{7x+2016}{2017} \] where \(x\) is a positive integer and \(x \leq 300\). There are certain values of \(x\) for which the fractions above can be expressed in such a way that the numerator and denominator are coprime (i.e., their greatest common divisor is 1). Determine the sum of all such values of \(x\).