Sum of all integral values of a belongs [1, 500] for which the equation as a [x]^3 + x - a = 0 has a solution ([.] denotes the greatest integer function) is ?
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[x]3 + x - a = 0
x = a - [x]3
a is an integer
[x]3 is an integer
x is an integer
a = x + [x]3
for x = 0, a = 0
for x = 1, a = 2
for x = 7, a = 350
for x = 8, a = 520
Therefore the required sum is