Root Retrieve App Files ???

[dkl1]

Here's the deal -

Broken LG G3 rooted (took a pretty hard drop)
No screen function
LED light flashes - nothing else

Going to get new device but will KEEP IT STOCK and will need the data from a business mileage app I've been using for a couple years. I'm cheap and I chose NOT to pay a monthly fee to use their cloud storage and simply kept my backups on the device. Is there any way I will be able to retrieve the files? Give it to me straight...

 

[Mikestony]

usb debugging enabled I would assume?
There may be some ADB commands to use or perhaps this may help?:
http://joyofandroid.com/unlock-android-device-with-dead-screen/