First image shows example of non accessible room. You need to destroy fractured wall which connects to it.
TLDR: Room with two connections contains fractured wall.

You must know 1/3/4 rule. In azurite mine rooms have only 1, 2 or 4 connetions and rooms with 2 connetions contain path to hidden room. This rule not affect original Niko's mineshaft.
Room with green circle has two connections.
Rooms with red circle have 1/3/4 connections.

Teleport to location which contains two connections and move to correct direction. (In this example I must go South)

Red arrows shows main connections.
Green arrows leads to fractured wall.

Here it is.
Destroy it and go back to minecart.

Now you can delve to desirable room.

Hexasam 14 Jun @ 1:35pm
"To add to this, if there are no nodes with only two connections near a hidden node, check the nodes with three connections, as nodes with one or four connections cannot have a hidden wall."

GLHF
May the toucan be with you.