Miguel Angel Romero Munguia, the 13th Root Mental Champion

Mexican psychiatrist Miguel Angel Romero Munguia is probably the fastest individual calculating 13th rooth.

Here we see his talent: https://www.youtube.com/watch?v=jl9REOScxV8.

But in Spain we have a Mathematics graduate which is good too in calculating 13th roots.
Here we can see the show of Gonzalo Orellana Barrasa: https://www.youtube.com/watch?v=q6ylacbOalA.

For interested in calculating this kind of root you can read https://deadreckonings.files.wordpress.com/2011/10/13throots.pdf

This is quite incredible. Is there a method known for calculating large roots such as this?