Root.m

With[{α = 1/5 ArcCos[(255300649 + 251245525 Sqrt[5])/857435524], 
   β = Sqrt[25085 - 6802 Sqrt[5]]},
 With[{γ = 1079441 (55 - 14 Sqrt[11]) + 
     98131 (-365 - 38 Sqrt[5] + 107 Sqrt[11] + 9 Sqrt[55]) Cos[α] - 
     811 (39510 - 14118 Sqrt[5] - 12837 Sqrt[11] + 3179 Sqrt[55]) Cos[2 α] + 
     121 (-2474 - 1479 Sqrt[5] + 763 Sqrt[11] + 385 Sqrt[55]) β Sin[α] + 
	 (22127 + 140925 Sqrt[5] + 3421 Sqrt[11] - 35431 Sqrt[55]) β Sin[2 α]},
  With[{η = 23747702 (-33 + 20 Sqrt[11]) - 
      98131 (-2453 + 2035 Sqrt[5] + 505 Sqrt[11] + 113 Sqrt[55]) Cos[α] - 
      17842 (-146174 - 13325 Sqrt[5] + 37995 Sqrt[11] + 1031 Sqrt[55]) Cos[2 α] + 
      121 (166573 + 3025 Sqrt[5] - 49167 Sqrt[11] - 2979 Sqrt[55]) β Sin[α] - 
      22 (-576143 - 229934 Sqrt[5] + 195022 Sqrt[11] + 64418 Sqrt[55]) β Sin[2 α] + 
      726 Sqrt[133815 γ]},
   1/32383230 (1079441 (-3 + Sqrt[11]) + 11 2^(1/3) 44605^(2/3) η^(1/3) + 
      17842 (-638 - 22 Sqrt[5] + Sqrt[11] + 63 Sqrt[55]) Cos[α] - 
      811 (-5479 + 3061 Sqrt[5] + 4723 Sqrt[11] + 1341 Sqrt[55]) Cos[2 α] + 
      44 (1397 + 132 Sqrt[5] - 466 Sqrt[11] + 122 Sqrt[55]) β Sin[α] +
	  (46291 + 43551 Sqrt[5] - 9923 Sqrt[11] - 9501 Sqrt[55]) β Sin[2 α] + 
      11 2^(2/3) 44605^(1/3) η^(-1/3) (-2158882 (-11 + 2 Sqrt[11]) - 
         8921 (-3179 - 143 Sqrt[5] + 798 Sqrt[11] + 180 Sqrt[55]) Cos[α] - 
         811 (15896 - 1642 Sqrt[5] - 6967 Sqrt[11] + 1035 Sqrt[55]) Cos[2 α] + 
         11 (-13673 + 2431 Sqrt[5] + 4514 Sqrt[11] + 120 Sqrt[55]) β Sin[α] + 
		 (-172406 - 140252 Sqrt[5] + 23673 Sqrt[11] + 31171 Sqrt[55]) β Sin[2 α]))]]]