Changing the Internet setting for IPv6 on your AirPort Extreme might help keep your Internet connection more stable, but it will also disable any IPv6 service that might be available on the Cox system. Connection speed and security are not affected.
Another way of saying the same thing is that your AirPort Extreme will behave the same way that it did before Cox began to incorporate the recent IPv6 changes into their system. Prior to Cox implementing IPv6 changes, there were no issues with Apple routers.
Apparently, Cox has made a decision to implement IPv6 into their system differently than other providers, and this is causing issues with Apple routers. I do not know if other brands are affected.
Whether this is an Apple issue or a Cox issue is open to question, but it might be worth noting that Comcast and Time Warner users are not having these same IPv6 issues with Apple routers, while we see multiple posts from Cox users almost daily.
I've had IPv6 up and running on a Time Warner connection here for about six months with zero issues. A friend who has Comcast service reports the same.
As far as I can tell, Apple has not made any statements on this issue, so it is not possible to say at this time whether the issue is all on Apple, part on Apple and part on Cox, or Apple is not actively involved in the issue at all.