halp

It should be $81+256=337.$ First, change the fourth root into $\frac{1}{4}.$

Now, without words:

$x^{\frac{1}{4}}=\frac{12}{7-x^{\frac{1}{4}}}$

$x^{\frac{1}{4}}\left(7-x^{\frac{1}{4}}\right)=\frac{12}{7-x^{\frac{1}{4}}}\left(7-x^{\frac{1}{4}}\right)$

$x^{\frac{1}{4}}\left(7-x^{\frac{1}{4}}\right)=12$

Expand, $7x^{\frac{1}{4}}-\sqrt{x}=12$

$7x^{\frac{1}{4}}-\left(x^{\frac{1}{4}}\right)^2=12$

Plug variables instead of $x^\frac{1}{4}$

to get $x=81,\:x=256$

Thus, te answer is $81+256=\boxed{337}.$

Let's see hoe tertre arrived at his solution

7x^(1/4) - ( x^1/4)^2 = 12     multiply through by -1

(x^1/4)^2 - 7(x^1/4) = -12

(x^1/4)^2 - 7(x^1/4) + 12 = 0         let  x^1/4 = a     and we have

a^2 - 7a + 12 = 0     factor

(a - 4) (a - 3) = 0      

Setting both factors to 0 and solving for "a" gives   a =4   or a = 3

So

x^1/4 = 4         or       x^1/4 = 3      take each side to the 4th power

x = 256          or       x =  81

And the sum of these is 337.....just as tertre found !!!!!