(Im)possible to construct

$\large a^3+b^5+c^7+d^9+e^{11}$

For positive integers $a,b,c,d$ and $e$ , determine the number of positive integers (greater than 1000) that cannot be represented by the expression above.

Details and Assumptions

• If you think all numbers can be represented this way, enter your answer as 0.
• If you think there are infinitely many numbers that cannot be represented this way, enter your answer as 9999999.