It sounds to me like Fluent Automation is itself referencing an older version of Newtonsoft.Json (4.5.0.0), and you say you are using the latest, which I believe is 6.0.1 Have you tried bindingRedirects?
Here's an example, it goes in your web.config/app.config:
<runtime>
<assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1">
<!-- Any other dependentAssembly bindings you need -->
<dependentAssembly>
<assemblyIdentity name="Newtonsoft.Json" publicKeyToken="30ad4fe6b2a6aeed" culture="neutral" />
<bindingRedirect oldVersion="0.0.0.0-6.0.1.0" newVersion="6.0.0.0" />
</dependentAssembly>
</assemblyBinding>
</runtime>