Error 401 Unauthorized MVC .NET WEB APP - asp.net-mvc

Question

I am working with an API that wants me to send the token along with Header, specifically Content Header.
Here is my code block.
string path_current_user = "me";
var cookie = HttpContext.Request.Cookies.Get("cookietoken");
string cookie_with_token = "ACCESS_TOKEN="+cookie.Value+";";
client.DefaultRequestHeaders.Add("Cookie", cookie_with_token);
client.DefaultRequestHeaders.TryAddWithoutValidation("Content-Type", "application/json; charset=utf-8");
client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("*/*"));
HttpResponseMessage response = await client.GetAsync(path_current_user);
I always get a 410 Unauthorized response. However, during debugging I can collect the values from the client object, and copy paste them into https://www.hurl.it, and I get the expected 200 OK response. So, I know the values that are being stored in the above code are correct. Its not a credentials issue for sure.
I have looked at almost 50 different threads on stack overflow, but none of them talk about this specification situation. Doing a GET with the Header Content set. Here is a screenshot of the HURL that works just fine.
Update 1 - Here is the API documentation for what I am trying to achieve.
Endpoint
GET me
Request Route
GET me
Headers
Content-Type: application/json Cookie: ACCESS_TOKEN="token characters
come here and remove the quotes"; Host: x.x
Update 2 - One of my mentors, recommended the following.
using (var httpClient = new HttpClient())
{
var request = new HttpRequestMessage(HttpMethod.Get, "https://small-project-api.herokuapp.com/me");
request.Headers.Add.("Content-Type", "application/json");
request.Headers.Add.("Cookie", cookie_with_token);
var response2 = await httpClient.SendAsync(request);
var responsestring = await response2.Content.ReadAsStringAsync();
}
He is of the opinion that may be such a request, as mentioned below, simply won't work in dot net. I am all but ready to give up here.