Water is leaking out of an inverted conical tank at a rate of $7800$ cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height $11$ meters and the diameter at the top is $3.5$ meters. If the water level is rising at a rate of $30$ centimeters per minute when the height of the water is $4.5$ meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Your answer: cubic centimeters per minute.