How do I get into the coal shaft in the Ancient Mine?

In the Ancient Mine there is a fence which I can't get past. By setting off some explosives and knocking a ramp over, I managed to find an alternate route where I was ambushed by some kind of floating worm monster. Just past this is a mine cart on a short track and a coal shaft which I'm guessing I need to enter to progress, but I can't figure out how to climb up into it.

(Can't believe I managed to get stuck no more than 30 minutes into the game...)

You are supposed to push the cart close to the mineshaft that is high up. Then to the left of that is a gear on the wall that you have to approach and use your action button to turn the gear. That should lower a ramp, you can then climb up onto the cart and into the mineshaft.

You can also watch a walkthrough video of this. It starts at 5:18

If it's the minecart filled with dynamite you certainly don't want to ride it (in fact there is no minecart ride anywhere, sorry to disappoint you there). Instead, blow it up (there's an explosive plant next to it) as well. Then it will roll towards the bridge (or some crystals blocking the way? sorry, it's been a while...) and you can move on.

edit As said it's been a while, but now I think I remember: You have to push the cart closer to the explosive bubbleplantthingies and then shoot them on the cart. This will case the dynamite to burn while the cart (automatically) rolls towards the obstacle and then explodes at the correct position.