Can I ask where you're located?
Edit: the reason I ask is because of issues like this, from
AT&T's International Roaming FAQ:
Q. How am I charged for voicemail calls while roaming internationally?
A. Voicemail calls are charged as follows:
When your device is on:
Calls that you do not answer that are routed to the AT&T voicemail system
will be charged as an international roaming incoming call to your device.
In addition, the foreign carrier's routing of that call to the AT&T voicemail system
may generate an outgoing call charge from your device's location to the U.S.
These charges apply even if the caller disconnects from the voicemail system without leaving a message.
If your device is turned off or in flight mode and the wireless network is off:
When someone tries to call you, the call will go directly to your personal voicemail greeting.
Since the network does not try to deliver the call to you in a foreign country, there are no international roaming charges.
When receiving Visual Voicemail messages on your smartphone or Apple? iPhone?:
Visual Voicemail messages received when roaming outside of the U.S.
will be charged at international roaming data rates, either at the international pay-per-use data rate or against your smartphone or iPhone international data package.
Now, I'm not an expert, and it could be that turning off Data Roaming does indeed curtail some of these charges?but I would definitely double check with my carrier before leaving.