You might find problems removing the nail with the slate ripper.
How to repair a slate roof leak.
Or see slate roof repairs for a discussion of permanent slate roof repairs rather than the leaky slate roof holding action discussed in the article above.
Or see these.
With good wire cutters you might also be able to cut off the head of the nail which will help.
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To do this use the slate ripper to rip off the nail that hooks the slate onto the slate roof.
Installing a bonding gutter this video shows a roof repair and the fitting of a bonding gutter between a slate and a tiled roof but it will also fit two slate roofs together as well.