How to calculate and power supply multiple led strips
If these LEDs have electronics integrated to control the brightness of the individual LEDs independently, connecting them in series is not an option for a number of reasons (data signals to control the brightness will need to be at the same voltage, for one). In such a situation, your calculation of 10.8A @ 5V is correct for 3 meters of strip.

It's worth noting that the power (18W/m) sounds like a maximum rating. In general, the power consumption at any point in time will depend on the brightness of the individual LEDs.