Am I Related to the Brothers Grimm?

Welcome to Valentine Grimm, my Etsy-sellin' entity. I'm not Valentine Grimm but my great-great-great-grandfather was, according to research conducted by my (older, always prettier, far more talented, but still - older) sister. So I started wondering: are we related to the brothers of fairy tale fame?

Wikipedia states that Jacob and Wilhelm Grimm were born in 1785 and '86 respectively, and raised in Hanau, Germany. If I read my sister's notes right, Valentine was born about 15 years earlier in the village of Unkenbach, which is about 125 kilometers due west of Hanau. 

Seems pretty close to me. However, my Friend Who Knows Everything points out that, back before the introduction of the horseless carriage, most people never traveled more than 20 kilometers from their place of birth. 

So Valentine never met Jacob and Wilhelm, and anyway he came to America and settled in Pennsylvania Dutch country. But I will still harbor the fantasy that they were distant cousins even though I know I'm peasant stock, through and through.