Scrolling Scroll Rect with Buttons

I am trying to create something like the following for my level selection


(taken from bing)

So, I want to allow the player to scroll through the levels by clicking/holding the left/right arrows.

By using Scroll Rect I can create something like this easily. However, I don't see a way to implement the buttons instead of a drag or scrollbar.

I tried creating two Buttons at a higher level than the Scroll Rect (so they aren't...

Scrolling Scroll Rect with Buttons