In the online Civil War Soldiers and Sailor's System I find a Benjamin F. White in the 49th Tennessee which contained two companies from Dickson County, he being listed a Pvt. in Company A, and in the book Tennesseans in the Civil War Part 2, I find a Benjamin White, Pvt., in Co A of the 49th Regiment, and a Benjamin White in Co. A of the 11th Regiment, also having men from Dickson County. There was no listing of him in the 11th Regiment in the online source I quoted above. It is possible these listings are the same man, although Benjamin White is a quite common name. If you know his middle initial it might be helpful. I have included two links below for you. Hope this helps.

http://www.itd.nps.gov/cwss/
http://www.tngenweb.org/civilwar/csainf/csa49.html