The earthwork editing facilites are accessed by clicking the button on the main toolbar. (See here for more details)
To move an entire earthworks design, click the button on the earthwork toolbar.
Once in the command, left once on a reference point to indicate the translation origin. Now when you move the mouse it will show a preview of where the earthwork will move too. Then simply left click again to pick the destination point for the translation and the entire earthwork will move and any interfacing will automatically update.
If you want to type in translation values, right click and choose Enter Values...
The above window will show where you can pick X, Y and/or Z translation values. Clicking OK will apply the entered values and the entire earthwork will move and automatically update.