For a positive number a, let the function f(x) be defined as:

f(x) = (x² - ax) / e^x

For a real number t, let g(t) be the number of distinct real roots x of the equation:

f(x) = f'(t)(x-t) + f(t)

Given that g(5) + lim_{t→5} g(t) = 5 and lim_{t→k⁻} g(t) ≠ lim_{t→k⁺} g(t), 

let the sum of all real numbers k that satisfy the discontinuity condition be q/p. 

Find the value of p + q, where p and q are coprime natural numbers.


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