\(y - 11\sqrt{y} + 24 = 0 \implies y + 24 = 11\sqrt{y}\)

Squaring both sides,

\(y^{2} + 48y + 576 = 121y\)

\(y^{2} + 48y - 121y + 576 = 0 \implies y^{2} - 73y + 576 = 0\)

\(y^{2} - 64y - 9y + 576 = 0\)

\(y(y - 64) - 9(y - 64) = 0\)

\((y - 9)(y - 64) = 0\)

\(\therefore \text{y = 64 or y = 9}\)