In a parallelogram, opposite sides are equal in length. Given that \( WZ \) is a side of the parallelogram and \( XY \) is its opposite side, we can set the equations for these sides equal to each other:
\[ WZ = XY \]
Substituting the expressions for \( WZ \) and \( XY \):
\[ 4s + 25 = 10s - 11 \]
To solve for \( s \), we can first rearrange the equation to isolate terms containing \( s \) on one side. We will move \( 4s \) to the right side and \( -11 \) to the left side:
\[ 25 + 11 = 10s - 4s \]
Combining the constants and the \( s \) terms gives us:
\[ 36 = 6s \]
Next, we divide both sides by 6 to find \( s \):
\[ s = \frac{36}{6} = 6 \]
Therefore, the value of \( s \) is:
\[ \boxed{6} \]