Joe and JoAnn each bought $12$ ounces of coffee in a $16$ ounce cup. Joe drank $2$ ounces of his coffee and then added $2$ ounces of cream. JoAnn added $2$ ounces of cream, stirred the coffee well, and then drank $2$ ounces. Find the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee. The answer is in the form \(\frac{k}{m}\). Please provide the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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