A bowl is created by taking the graph $\displaystyle y=\frac{x^4}{100}$ from $\displaystyle x=0$ to $\displaystyle x=6$ and revolving it around the y-axis. Milk is being poured into the bowl at a constant rate of 200 cubic feet per minute. A crack in the bowl appears when the milk reaches a depth of 5 feet, causing milk to leak out of the bowl at 30 cubic feet per minute. What is the rate of change in the depth of the milk when the milk reaches a depth of 12 feet?