Add numbers found in text in multiple cells

This is a tad complicated.

I have a table with text.

Column one has cells with text that contain numbers and text.
I want to find all cells that start with a certain string, find the number that preceeds a certain string and add them all together and store as numeric in another cell.

I have included an attachement with my best attempt so far. Column F is where I have the cells with the formula.

Help.