How Can i Root my HTC ONE X with android version 4.0.4, HTC sense version 4.0, Software number 2.20.502.7 ATT US edition
Apparently there is a root method for the AT&T One X running 4.0.4. I've not tested it, but have reproduced the instructions in full from here:
I have successfully rooted the AT&T HTC One X running build 2.20.
In the previous build (1.85), S-ON was only partially enforced, so it was possible to modify the /system partition without having unlocked the bootloader, in order to install su and Superuser.apk. This was changed in build 2.20: full S-ON is now in effect. As a result, it is no longer possible to write to /system even after remounting it as writable, since the S-ON feature has NAND-locked the storage.
In other words, it's impossible have a "permanent root" on 2.20 in the traditional sense without unlocking the bootloader.
I have prepared an exploit that gains temporary root access by leveraging two vulnerabilities and uses these newly gained root privileges to overwrite the CID ("superCID"), so that it's possible to unlock the bootloader via HTC's website. I'm sorry if you'd prefer to not unlock your bootloader this way, but there are no other options for root access available.
This exploit modifies the CID of your device. Doing so likely voids your warranty, and may be in violation of your contract with AT&T (I am not a lawyer). Additionally, while this exploit has been tested and has not been observed to cause any negative side effects in practice, I am in no way responsible if it turns your device into an expensive paperweight.
I am not affiliated with any Android forum or group, including XDA - this is just where I've chosen to publish this exploit.
Portions of this exploit are similar in concept to the ADB backup/restore exploit published by Bin4ry, but the vulnerability used in this exploit is entirely distinct from Bin4ry's.