If you used this jail break, then the update to 5.6.1.1 will 'just work'.
If it has been too long to be certain, install:
https://www.mobileread.com/forums/sh...68&postcount=4
It does no harm to install it, even if it is already installed (as it should be).
This jail break is "viral" it will self-reinstall when the Kindle re-boots after the update.
REALLY BIG NOTE:
I mean that quite literally, the jail break,
and nothing else is 'bridged' across Amazon updates. You (not just you, anyone) have to re-install everything else.
Your first choice for current packages is always:
https://www.mobileread.com/forums/sh...d.php?t=225030