There is no versioning hell. This is specifically the goal of NuGet: the different versions of the same package can be installed side by side. The only limitation is that you can't reference different versions in the same project. But what versions of libraries are referenced by the packages I depend on are irrelevant for my project.
In most cases, you can't even avoid this situation if you use third-party libraries. Imagine you depend on third-party library A and third-party library B. The A library uses a specific version of Json.Net. The B library uses another version. What do you do? Do you ask the author of one of those libraries to upgrade or downgrade the dependencies? Do you throw one of the libraries and spend the next two years rewriting it just to use a specific version of Json.Net?
As an author of a library, you shouldn't care about the version of Json.Net your customers use in their projects, or about the versions of Json.Net used by third-party libraries, because you won't get it right anyway. One customer will use the version 6; another—version 8. Your library will be installed side by side with other libraries using version 7 and the ones using version 9.
This is for cases when people install my package, but don't have the latest version of Json.Net - not to force them to update their references.
This works in a rare case of people who are using the 6.0.1 version of the library. And fails for everyone who uses the version 6.0.0. And 5.*. And 4.*. And 6.0.2. And 6.0.3. You get the picture.
The only thing you should care of is the image you give of your project. If you're using an outdated version, people could think:
Ew, this looks old. Why is this guy using a library which is not used any longer for the last three years? I think he just doesn't maintain his project any longer. I'll try one which is actually maintained.
On the other hand, if you're using the most recent version of a third-party library, what could happen? The person could find that your library is using a newer version, and decide to update her own project. Or continue using the old version, because this too is a valid choice.