Adverbs acting as manner adjuncts “do not occur between whether and infinitival to,” you guys. Duh.
Or, in other words, you can’t say, “…decide whether unconditionally to attend the Geneva talks.” Instead, you should say, “…decide whether to unconditionally attend the Geneva talks,” because that “rule” about split infinitives doesn’t actually exist.
Geoffrey Pullum explains this and more in a delightful piece for the Chronicle of Higher Education which proves that sometimes being stringent about grammar is easier than you think (for everyone except certain peevish copyeditors).