To solve this problem, we need to analyze the sequence of figures and identify the one that deviates from the established pattern. Let’s go through the solution step-by-step:

1. Examine each figure and look for a repeating pattern. The pattern often involves shapes, colors, or arrangements that are consistent across the series.
2. Upon closer inspection, we can observe that each figure alternates between white and black squares in a set pattern.
3. The pattern follows: white square, black square, white square, black square, etc.
4. Look closely at each provided option: $3^{rd}$, $6^{th}$, $9^{th}$, and $11^{th}$ figures. Each of them should follow the above pattern except for the one that breaks it.
5. Let's specifically compare the $11^{th}$ figure with the others. It has a disruption in the color sequence in comparison to the rest of the figures.
6. As observed, while all other figures maintain the alternating color sequence, the $11^{th}$ figure disrupts this continuity, hence breaking the pattern.

Hence, the figure that breaks the pattern is the $11^{th}$ figure.