There is a way to make your Toshiba BDX1100KB or BDX1100KE play region A blu-rays. What you can do is to install the region A firmware. It sounds like much work but it is actually done in about half a minute (if you use SD-card).
First I will recommend you to upgrade to the latest version (V50) if you are not already there.
For Toshiba BDX1100KB:
Toshiba : Download Centre : BDX1100KB
For Toshiba BDX1100KE:
Toshiba : Download Centre : BDX1100KE
Save the 2 files you get from running the exe-file to a subfolder called UPG_ALL on a CD or SD-card. Put it in your player and do the upgrade if you are on a lower version number. Label the CD or SD-card 'Region B'.
Then download the V50 region A firmware:
https://rapidshare.com/files/8305187...00_RegionA.zip
Unzip the firmware file within the zip file to a folder called UPG_ALL on another CD or SD-card. Label it 'Region A'.
When you want to play a region A blu-ray (or region 1 DVD), put first the CD or SD-card in the player and change the region. It will stay region A until you change it back to region B by using the CD or SD-card with region B firmware.
As Jasiel says in a post further down, there is also a possibility to flash the BDX1100 with BDX1105 regionfree firmware. Making the player regionfree for both DVD and blu-ray. Instructions and link to firmware can be found in this thread:
Toshiba BDX1100, regionfree DVD and multiregion BD