Silene maritima roots

For various reasons. like bad backs, bad knees,bad weather and such like, one area of one of our rock gardens has been swamped by Silene maritima and Phlox Oakington Blue eyes (and this is an area of about 15 sq metres). So now I am slightly fit I was in the process of clearing it, but I was wondering if the roots of either of these are' persistent'? Dandelion roots are persistent, but Creeping buttercups are not (as long as you remove all the growing points).
Anyone any experience of clearing these plants out?