I am not aware dennikn.sk would have English, in case you want mainstream Slovak news not in English then sme.sk or aktuality.sk are the most popular sites (not tabloid), though all of these 3 have mostly paid articles, which is why I recommended rtvs which is free
I switched the site to use sme.sk. I'll need to re-evaluate if I do want to use an English site first vs using the most popular site and translating it. The latter will be a better representation.