What is the value of \( x \) ? \[ \sin (x+11)^{\circ}=\cos (2 x+22)^{\circ} \] Enter your answer in the box. \[ x=(1) \]

Step 1 ：\sin{(x+11)^{\circ}}=\cos{(90^\circ-(x+11)^\circ)}

Step 2 ：\cos{(90^\circ-(x+11)^\circ)}=\cos{(2x+22)^\circ}

Step 3 ：90^\circ-(x+11)^\circ=2x+22^\circ

Step 4 ：x=\frac{57^\circ}{3}