Order by sum of digits of number

Example:

a = "56 65 74 100 99 68 86 180 90", ordered by numbers weights becomes: "100 180 90 56 65 74 68 86 99"

When two numbers have the same "weight", let us class them as if they were strings and not numbers: 100 is before 180 because its "weight" (1) is less than the one of 180 (9) and 180 is before 90 since, having the same "weight" (9) it comes before as a string.

All numbers in the list are positive numbers and the list can be empty.

My tests:

[TestMethod]
public void Test1()
{
     Assert.AreEqual("2000 103 123 4444 99",
         WeightSort.orderWeight("103 123 4444 99 2000"));
}

[TestMethod]
public void Test2()
{
    Assert.AreEqual("11 11 2000 10003 22 123 1234000 44444444 9999",
        WeightSort.orderWeight("2000 10003 1234000 44444444 9999 11 11 22 123"));
}

My class to calculate the order of the weights:

public class WeightSort
{
    public static string orderWeight(string strng)
    {
        List<int> list = strng.Split(' ').Select(Int32.Parse).OrderBy(i => i).ToList();
        List<int> SumofNums = new List<int>();
        List<string> SumandNums = new List<string>();
        List<string> SumandNums2 = new List<string>();
        List<string> Nums = new List<string>();

        foreach (var itm in list)
        {
            int num = (int)GetSumOfDigits(itm);
            SumofNums.Add(num);
            SumandNums.Add(itm + "," + num);
        }
        SumofNums = SumofNums.OrderBy(i => i).ToList();
        string txt = "";            
        foreach (var itm in SumofNums)
        {
            var item = itm.ToString();
            if (!Nums.Contains(item))
            {
                foreach (var itm2 in SumandNums)
                {
                    var itm3 = itm2.Split(',');
                    if (item == itm3[1])
                    {
                        SumandNums2.Add(itm2);
                        if (string.IsNullOrEmpty(txt))
                            txt = itm3[0];
                        else
                            txt = txt + " " + itm3[0];
                    }
                }
                Nums.Add(item);
            }            
        }

        return txt;
    }

    static long GetSumOfDigits(long n)
    {
        long num2 = 0;
        long num3 = n;
        long r = 0;
        while (num3 != 0)
        {
            r = num3 % 10;
            num3 = num3 / 10;
            num2 = num2 + r;
        }

        return num2;
    }
}

I can handle if there is only one but not duplicates. Please help me rewrite my class so it can handle the duplicates also..

Sum of digits:

string weights = "103 123 4444 99 2000";

1) 2000, digit sum = 2;
2) 103, digit sum = 4;
3) 123, digit sum = 6;
4) 4444, digit sum = 16;
5) 99, digit sum = 18;

the correct order is "2000 103 123 4444 99"