I walked into the mine and just couldn't see anything because the roof was in the way :(
When you pick up the pickaxe, you need to go to the mine (there is an arrow around the player that shows the direction, also you can use minimap) and than you will see slight fade to black screen and back to normal -> that means that you completed the task and you can continue doing other tasks.
If you have any more questions, feel free to ask.
Best regards, Dwarven group.