Is there a root method for 4.5.5

I just inherited a 3rd Gen Kindle Fire HDX 7" that is running latest firmware (4.5.5). I am a newb to Kindle but not Android devices

I want to run some apk not available in Amazon Apps (Guitar apps) . Is there a way to root this newest firmway to get google play store as well as Amazon's store. If not, can I side load APKS if I have them. I was surprised to see when I connected to my computer, I couldn't access directories - Is therer a way to access the system directories to sideload apks or do I need to email them/dropbox them etc?

Just not sure what I can do withthe 4.5.5 firmware as it seems like the latest updates are hard to modify.

Any advice would be appreciated.

Thanks,
Michael