And, depending on the cell towers, GSM communication simply doesn't work for two reasons at those altitudes:
1. Cell tower transmitters and receivers are placed in a 3 x 120° configuration, angled slightly downwards to give optimal signal strength. This is why it's nearly impossible to obtain a signal from a cell tower if you stand right at it. These are the most common configurations.
2. Another fairly common configuration are with omni-directional receivers and transmitters. Those are usually used in areas with a very uneven landscape. You're actually able to communicate full duplex with them at 30,000 feet. Problem is that it's nearly impossible to only register with one cell-tower which renders the service invalid. IMEI numbers are as a standard blocked from the service when there's a handshake from multiple towers from the same device.
(I've been working with telecom tech for 9 years)